Include examples in type checking

Remove `examples/` from the `pyrightconfig.json` ignore list and fix
the resulting type errors across all example files. Common fixes:

- Required API keys: `os.getenv("X")` -> `os.environ["X"]` so the
  return type is `str` rather than `str | None`, and misconfiguration
  fails fast.
- Narrow `LLMContextMessage` union members with `isinstance(..., dict)`
  before dict-style access.
- `assert isinstance(params.llm, ...)` before calling service-specific
  methods that aren't on the base `LLMService`.
- Guard optional frame fields (e.g. `LLMSearchResponseFrame.search_result`)
  before use.

examples/persistent-context/persistent-context-grok-realtime.py

@@ -192,7 +192,7 @@ Remember, your responses should be short - just one or two sentences usually."""
     )
 
     llm = GrokRealtimeLLMService(
-        api_key=os.getenv("XAI_API_KEY"),
+        api_key=os.environ["XAI_API_KEY"],
         session_properties=session_properties,
     )